The Compton Scattering Total Cross Section at Next-to-Leading Order

Abstract

An analytic formula is given for the total scattering cross section of an electron and a photon at order ${\alpha }^3$. This includes both the double-Compton scattering real-emission contribution as well as the virtual Compton scattering part. When combined with the recent analytic result for the pair-production cross section, the complete ${\alpha }^3$ cross section is now known. Both the next-to-leading order calculation as well as the pair-production cross section are computed using modern multiloop calculation techniques, where cut diagrams are decomposed into a set of master integrals that are then computed using differential equations.

6 pages 1 figure; v2. published version; explicit expressions given in an Appendix and in Mathematica notebook